**1. Introduction**

Smart grid is a modern grid infrastructure with high efficiency, reliability, and safety, which is based on renewable energy, automatic control, and modern communication technology [1,2]. An ancillary service is indispensable in an electric service, and plays a vital role in providing strong support for power transmission and power system operation. Ancillary service includes services related to frequency stability. The stability of grid frequency is closely related to the operation of power market and the equipment safety of the power generation side and power consumption side. Ancillary service mainly includes: Frequency adjustment, automatic generation control, spinning reserve, and peaking services.

The mismatch between the power supply side and the area power consumption can affect the frequency of the power system. Hence, the load frequency regulation is necessary in power systems, in order to maintain power balance under normal conditions [3]. Grid frequency can be used to evaluate power quality. The main way to adjust the frequency of the power system is to change the generated output power and manage the loads in demand side. Reasonable control of temperature control loads can provide adjustable buffer energy for power systems [4]. A grea<sup>t</sup> deal of potential electrically-thermal energy is stored in all sorts of heat buffers equipment, such as heating, air conditioning units, and fridges [5]. The advantages of aggregated thermostatically controlled loads (TCLs) to take part in power grid frequency regulation are as follows: Firstly, the TCLs which can store massive energy are of wide distributions; secondly, the control method of them is simple, fast, and real-time; thirdly, the aggregated TCLs can generate a continuous reaction without considering the discrete characteristics of the individual load

control [6]. The managemen<sup>t</sup> of TCLs is one of frequency adjustment strategies with extremely high feasibility to ensure frequency stability and improve power quality.

Recently, the bilinear partial differential equation (PDE) model was developed to provide effective control of aggregated TCLs [7]. Two control methods, based on the combination of estimator and controller, were utilized to control TCLs and effectively track demand curve [8]. A centralized and distributed algorithm based on the state space model of heating ventilation and air-conditioning (HVAC) was proposed to reduce power fluctuations and improve satisfaction of demand side [9]. A model predictive control was described and applied to demand-side response services in [10]. A distributed model predictive control (DMPC) method based on an optimized aggregation model was applied to provide frequency regulation services [11]. A Fokker–Planck diffusion model and a direct load control algorithm were developed in [12]. A model of aggregate homogeneous TCLs with uniform variation of temperature set-point was developed, and a linear quadratic regulator (LQR) has been designed in [13]. In [14], the authors proposed a novel causal method based on a parametric second-order model to forecast the energy conservation. In [15], a linear optimization model was built to provide frequency regulation services for power systems while also providing short-term demand response management. In [16], the authors proposed several switched control strategies for aggregate HVACs to provide demand-side frequency regulation. Although various aggregation characteristics of TCLs have been extensively studied, modeling precision still needs to be farther improved. As a matter of fact, it is hard to establish accurate mathematical models or physical models for aggregated TCLs because of various assumptions and computational complexity in the modeling process.

In recent years, artificial intelligence has developed rapidly with the characteristics of bionics and intelligence. This paper proposes a fuzzy neural network control method which adjusts TCLs based on the input and output data of TCLs instead of the aggregated TCL model. This method can reduce tracking errors and computational complexity, because it draws the advantages–logic reasoning capability of fuzzy control and self-learning capability of the neural network [17]. This study has the following contributions:


The rest of this paper is organized as follows. Section 1 introduces the thermal dynamics of individual TCLs and the frequency regulation problem. Section 2 describes the system structure, algorithm, and optimization of the fuzzy neural network control in detail. The simulation results are shown in Section 3. Finally, the conclusions are summarized in Section 4.
